Simultaneous Drawing of Layered Trees

Julia Katheder, Stephen G. Kobourov, Axel Kuckuk, Maximilian Pfister, Johannes Zink

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to permute the vertices on the other layers (respecting the given tree embeddings) in order to minimize the number of crossings. While this problem is known to be NP-hard for multiple trees even on just two layers, we describe a dynamic program running in polynomial time for the restricted case of two trees. If there are more than two trees, we restrict the number of layers to three, which allows for a reduction to a shortest-path problem. This way, we achieve XP-time in the number of trees.

Original languageEnglish (US)
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024, Proceedings
EditorsRyuhei Uehara, Katsuhisa Yamanaka, Hsu-Chun Yen
PublisherSpringer Science and Business Media Deutschland GmbH
Pages47-61
Number of pages15
ISBN (Print)9789819705658
DOIs
StatePublished - 2024
Event18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024 - Kanazawa, Japan
Duration: Mar 18 2024Mar 20 2024

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14549 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference and Workshops on Algorithms and Computation, WALCOM 2024
Country/TerritoryJapan
CityKanazawa
Period3/18/243/20/24

Keywords

  • crossing-minimization
  • dynamic program
  • layered drawing
  • tree drawing
  • XP-algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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